1994/12/12 by Chongying Dong, Dong, Chongying, Geoffrey Mason +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.hep-th/9412109
openalex publication_date 1994/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let V be a simple vertex operator algebra and G be a finite nilpotent group of automorphisms of V. We prove the following in this paper: (1) There is a Galois correspondence between subgroups of G and the vertex operator subalgebras of V which contain VG given by the map H↦ VH. (2) Assume that for every G∈ G there is unique simple g-twisted V-module M(g). Then there exists a Hochschild 3-cocycle α on the integral group Z[G] such that there is an equivalence of categories between VG-module category (whose objects are VG-submodules of direct sums of copies of ⊕g∈ GM(g), and whose morphisms are VG-module homomorphisms) and the module category for the twisted quantum double Dα(G) associated to α.